The principal's new car cost $\$ 35,000$ , but in three years it will only be worth $\$ 21,494$ . Write an equation for this situation and explain what each part of the equation represents in the context of the problem. What is the annual rate of depreciation?

View step-by-step help

Home

Math Problems

Grade 8

Solve a system of equations using any method: word problems

Full solution

Q. The principal's new car cost

\$ 35,000

, but in three years it will only be worth

\$ 21,494

. Write an equation for this situation and explain what each part of the equation represents in the context of the problem. What is the annual rate of depreciation?

Denote Equations: Let's denote the original cost of the car as $C_0$ , the value of the car after three years as $C_3$ , and the annual rate of depreciation as $r$ . We can write the equation for the depreciation of the car over three years as: $\newline$ $C_3 = C_0 - 3r$ $\newline$ In this equation, $C_0$ represents the initial cost of the car, $C_3$ represents the value of the car after three years, and $3r$ represents the total depreciation over three years.
Plug in Values: Now we can plug in the values we know into the equation: $\newline$ $21494 = 35000 - 3r$ $\newline$ This equation will allow us to solve for $r$ , the annual rate of depreciation.
Isolate and Solve: To find $r$ , we need to isolate it on one side of the equation. We'll start by adding $3r$ to both sides and then subtracting $21494$ from both sides: $\newline$ $3r = 35000 - 21494$
Calculate Difference: Next, we calculate the difference on the right side of the equation: $\newline$ $3r = 13506$
Divide and Find Rate: Now, we divide both sides by $3$ to find the annual rate of depreciation: $\newline$ $r = \frac{13506}{3}$
Divide and Find Rate: Now, we divide both sides by $3$ to find the annual rate of depreciation: $\newline$ $r = \frac{13506}{3}$ Performing the division gives us: $\newline$ $r = 4502$ $\newline$ So, the annual rate of depreciation is $$4502$.